Yeah, it wouldn't help, they don't weigh enough. However, if you are looking to spend money modifying it, you can get some lightweight tuners, and get a BAII bridge. But in my opinion you'd be better off getting a new bass.

use logic my man, lets say just the head stock on your bass ways ooooo, a pound not even, with tunning pegs and all. if you put a (proably in the onces range) piece of metal on the middle of your basses body its obviously not goin to do anything.

the head dive is on lots of fenders and other basses, that where there body doesnt counter balance the wieght of the head. its not always having a light head stock or a heavier body, its how the body is designed sometimes. so i wouldnt worry about it and just tough it out.

I don't know if this would help seeing as how I have never done it, but you could move the strap lock closest to your bridge down about 5 inches. If you type "Warwick Thumb neck dive" I am sure you will find some helpful solutions.

that's a link that talks about fixing neck dive on a t-bird. It does involve drilling, but it will probably work on a p-bass. You should proabably ask someone who is experienced with this kind of stuff first.